A) \[6\sqrt{3}\]cm
B) \[12\sqrt{3}\]cm
C) \[16\sqrt{3}\]cm
D) \[18\sqrt{3}\]cm.
Correct Answer: D
Solution :
(d):- Since, PQR is an equilateral. Then, PL is also the median of \[\Delta PQR\], Similarly RN and QM are also the median and 0 is the centroid. So, \[\frac{PO}{OL}=\frac{2}{1}\] \[OL=\frac{PO}{2}=\frac{9}{2}\]cm Now, Altitude of \[\Delta PQR=\frac{\sqrt{3x}}{2}\] (Where, \[x=\] length of side of equilateral \[\Delta PQR\]) \[PO+OL=\frac{\sqrt{3a}}{2}\] \[6+3=\frac{\sqrt{3a}}{2}\] \[a=\frac{18}{\sqrt{3}}=6\sqrt{3}\] \[\therefore \] Perimeter of \[\Delta PQR=3a\] \[=3\times 6\sqrt{3}=18\sqrt{3}\]cmYou need to login to perform this action.
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